Nonlinear free vibration of functionally graded graphene platelets reinforced porous nanocomposite plates resting on elastic foundation

This paper presents an investigation on free vibration of functionally graded (FG) porous nanocomposite plates reinforced with a small amount of graphene platelets (GPLs) and supported by the two-parameter elastic foundations with different boundary conditions. Four different porosity distributions of the parent metal were reinforced by four various GPLs dispersion patterns (evenly or unevenly) along the thickness direction. To obtain graded distribution in both porosity and GPLs, the Young's modulus, shear modulus and density of nanocomposites are assumed to vary through the thickness direction due to variation of internal pores and the volume fraction of GPLs. By employing Halpin-Tsai micromechanics model, effective elastic modulus of the nanocomposites is obtained according to the assumption of closed-cell cellular solids under Gaussian Random Field scheme. The governing equations of FG GPLs-reinforced metal foams resting on elastic foundations are derived from Hamilton's principle by the means of classic plate theory with the consideration of von Kármán strain-displacement relation. Applying the differential quadrature method, the dimensionless natural frequencies of porous nanocomposite plates with different boundary conditions are obtained and present method is thoroughly validated with the results in open literature. The comprehensive parametric studies on different porosity coefficients, GPL dispersion patterns, weight fraction of GPL, aspect ratios, thickness ratios and parameters of elastic foundation on free vibration of FG GPLs-reinforced porous plates with various boundary conditions. An interesting finding is that the increase of porosity coefficients would lead to the linearly decrease of both mass density and stiffness of the plates, but the increase of porosity coefficients does not always induce the decrease of natural frequencies. Moreover, both porosity distribution and GPL dispersion pattern have a distinct effect on dynamic characteristics, the former plays a more important role than the latter in analysing mechanical properties of FG GPLs-reinforced plates.